Krylov complexity in quantum field theory, and beyond
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13130_2024_Article_23686.pdf
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Author(s)
Avdoshkin, Alexander
Dymarsky, Anatoly
Smolkin, Michael
Date Issued
June 12, 2024
Journal
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Citation
Avdoshkin, A., Dymarsky, A. & Smolkin, M. Krylov complexity in quantum field theory, and beyond. J. High Energ. Phys. 2024, 66 (2024).
Version
Final published version
Abstract
We study Krylov complexity in various models of quantum field theory: free massive bosons and fermions on flat space and on spheres, holographic models, and lattice models with a UV-cutoff. In certain cases, we observe asymptotic behavior in Lanczos coefficients that extends beyond the previously observed universality. We confirm that, in all cases, the exponential growth of Krylov complexity satisfies the conjectured inequality, which generalizes the Maldacena-Shenker-Stanford bound on chaos. We discuss the temperature dependence of Lanczos coefficients and note that the relationship between the growth of Lanczos coefficients and chaos may only hold for the sufficiently late, truly asymptotic regime, governed by physics at the UV cutoff. Contrary to previous suggestions, we demonstrate scenarios in which Krylov complexity in quantum field theory behaves qualitatively differently from holographic complexity.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/jhep06(2024)066
